In material processing by application of laser radiation, laser beam scanning of the zones to be processed on the object is generally employed. The precision of positioning the laser beam usually determines the precision achieved in said processing. Focusing of the laser beam into a processing volume requires exact three-dimensional positioning. Therefore, for high-precision processing it is usually indispensable to hold the object in an exactly defined position relative to the laser processing device. The above-mentioned adapter is intended for such applications because it fixates the object to be processed or imparts a desired shape to the deformable surface of the object to be processed.